Stability results of a fractional model for unsteady-state fluid flow problem
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Author list: Thamareerat N., Luadsong A., Aschariyaphotha N.
Publisher: SpringerOpen
Publication year: 2017
Journal: Advances in Difference Equations (1687-1839)
Volume number: 2017
Issue number: 1
ISSN: 1687-1839
eISSN: 1687-1847
Languages: English-Great Britain (EN-GB)
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Abstract
This paper mainly focuses on a fractional model for unsteady-state fluid flow problem developed based on the meshless local Petrov-Galerkin (MLPG) method with the moving kriging (MK) technique as a background. The contribution of this work is to investigate the stability of a model with fractional order governed by the full Navier-Stokes equations in Cartesian coordinate system both theoretical and numerical aspects. This is examined and discussed in detail by means of matrix method. We show that the scheme is unconditionally stable under the restriction of eigenvalue. The dependence between several of the important parameters that impact on the solution is also studied thoroughly. In discretizing the time domain, an algorithm based on a fixed point method is employed to overcome the nonlinearity. Two selected benchmark problems are provided to validate the stability of the present method, and a very satisfactory agreement with the obtained results can be found. ฉ 2017, The Author(s).
Keywords
fixed point iteration, matrix method, time-fractional Navier-Stokes equations, unconditionally stable
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